In this paper, we propose a simple model that can determine the body’s Center of Mass through body indicators: height, weight and three other parameters of body’s measurement (sizes of Chest, Waist and Hip). From the measured data, a quick, stable and accurate model has been built, which reveals the relationship between the Center of Gravity (CoG) and the body indicators: weight, height and body measurements.
Journal of Science & Technology 139 (2019) 057-061 The models of Relationship between Center of Gravity of Human and Weight, Height and Body’s Indicators (Chest, Waist and Hip) Tran Anh Vu 1*, Hoang Quang Huy1, Nguyen Anh Tu1, Le Van Tuan1, Le Viet Khanh1, Pham Thi Viet Huong School of Electronics and Telecommunications, Hanoi University of Science and Technology, Hanoi, Viet Nam University of Engineering and Technology, Vietnam National University Hanoi, Hanoi, Vietnam Received: July 16, 2019; Accepted: November 28, 2019 Abstract Determining the position of the Center of Gravity (CoG) of the human body takes an important role in human movement analysis Recently, there are several measurement methods to estimate the center of body point These methods are generally costly, time consuming and complicated implementation process In this paper, we propose a simple model that can determine the body’s Center of Mass through body indicators: height, weight and three other parameters of body’s measurement (sizes of Chest, Waist and Hip) From the measured data, a quick, stable and accurate model has been built, which reveals the relationship between the Center of Gravity (CoG) and the body indicators: weight, height and body measurements Keywords: Vestibular disorder, center of gravity (CoG), body measurement Introduction used linear regression method to serve in data processing in thoracic ultrasound diagnosis [2] This paper investigates the relationship between body parts, namely weight, height, three sizes of body’s measurements and the CoG A body's Center of Gravity (CoG) is defined as the point around which the resultant torque due to gravity forces vanishes Determining the body’s CoG has many applications in recent years In medicine, knowing the central position helps us diagnose whether the person have vestibular disorders and other diseases In sports, in order to study the postures or movements of athletes, the focus is very important to set the standards of movements and to determine methods to achieve higher efficiency in competitions and treatment In literature, there are many methods for determining the focal points such as digitizing (the anatomical landmarks such as the shoulder, elbow, groin, pillow ) to create a 2D or 3D model of the body From there, they can calculate the focus of every part of the body and the whole body These methods are very costly and time consuming Our methods overcomes these challenges, which have the ability of finding a center of gravity (CoG) simply and less costly Method In this paper, we use linear regression analysis to determine the relationship between the CoG point along the body’s axis and the body’s measurements In other words, we can estimate the CoG of any given person if we know his/her body’s measurement with high accuracy 2.1 Data preparation In this phase, the measurement process is implemented Regarding the weight, height and sizes of body’s measurement, we collected data from people aged 19-23 Everyone is in normal health condition 90 measurements are recorded and stored in Excel Regarding the determination of the position of the CoG point along the body’s axis, we designed a specific scale that can give the position of the humans’ CoG The subject will be guided to the correct position, where their feet are placed at the original line as in figure 1, and relaxed body when lying on the system In the collecting data and processing phase, many methods are attemped to provide the best results with the simplest implementation Linear regression method has been used a lot in recent years due to its simplicity and accuracy For example, in 1995, accurate diagnosis and short-term surgery results in cases of suspected appendicitis in processing the collected data [1] In 2010, doctors Corresponding author: Tel.: (+84) 912.834.422 Email: huy.hoangquang@hust.edu.vn * 57 Journal of Science & Technology 139 (2019) 057-061 observations [3] In linear regression, the most concern is about uncertainty The uncertainty can arise from three main sources: (i) measurement uncertainty, inaccuracy in observations, (ii) uncertainty of measurement model, non-effects linearity and (iii) the uncertainty of the time structure in the parameters of the linear model or the appearance of non-linear components The general purpose of regression is to examize two things: (i) Does a set of predictor variables (X) a good job in predicting an outcome (Y) variable? (ii) Which variables in the set X are significant in determining/ predicting the outcome? Fig Position of subject laying on scale The proposed model includes a mechanical system designed so that the subject can lie on it Loadcells will be fixed at legs of this system as in figure Linear regression is often done to draw a model that can be used to make predictions about the future, and should therefore be designed to accommodate future "surprises" [3] Those 'surprises' are structural changes in the system that arise from market changes, from technological innovations or from certain disagreements By definition, nothing in historical data can reveal anything about future 'surprises' According to Frank Knight's definition [4] - the first to clearly distinguish risks including known probability measures, and Knight called true uncertainty A model is a group of unlimited nested events and no worst 'case' Information gap models provide a clear and minimal representation of ignorance of future 'surprises' Linear regression is essentially a regression analysis method of statistical probability L ���⃗ 𝐹𝐹2 ���⃗ 𝐹𝐹1 𝑋𝑋𝐶𝐶𝐶𝐶𝐶𝐶 ��������⃗ 𝐹𝐹𝐶𝐶𝐶𝐶𝐶𝐶 ���⃗ 𝐹𝐹4 ���⃗ 𝐹𝐹3 𝑥𝑥⃗ Fig The proposed scale model The support points and are placed at the original line (perpendicular with X axis), the coordinate X=0 The support points and are placed at the distance L from the original line (the frame length, 𝐿𝐿 = 1475 mm) The body’s mass F creates F1, F2, F3 and F4 forces on support points In this paper, we used SPSS software to perform the algorithm with linear regression algorithm To evaluate the model, it is necessary to pay attention to the following parameters: where F = F1 + F2 + F3 + F4 The coordinates XCoG (the coordinates of CoG point from foot) of the center of mass satisfy the condition that the resultant torque is zero: Correlation coefficients R: is an index of measurement statistics showing how strong a relationship is between two variables 𝑇𝑇 = � 𝑋𝑋𝑖𝑖 ��⃗ 𝐹𝐹𝚤𝚤 = 𝑖𝑖 Parameter R2 (R-squared): reflects the degree of influence of the independent variables on the dependent variable In other words, it reflects how close the data are to the fitted regression line (𝐹𝐹1 + 𝐹𝐹2 ) + 𝐿𝐿(𝐹𝐹3 + 𝐹𝐹4 ) − 𝑋𝑋𝐶𝐶𝐶𝐶𝐶𝐶 𝐹𝐹 = 𝐿𝐿(𝐹𝐹3 + 𝐹𝐹4 ) − 𝑋𝑋𝐶𝐶𝐶𝐶𝐶𝐶 (𝐹𝐹1 + 𝐹𝐹2 + 𝐹𝐹3 + 𝐹𝐹4 ) = CoG point along the body axis is calculated by formula below: 𝑋𝑋𝐶𝐶𝐶𝐶𝐶𝐶 = (𝐹𝐹1 + 𝐹𝐹2 ) ∗ Adjusted R-square: It is a modified version of R-squared, which has been adjusted for the number of predictors in the model The adjusted R-squared increases only if the new term improves the model more than would be expected by chance 𝐿𝐿 (𝐹𝐹1 + 𝐹𝐹2 + 𝐹𝐹3 + 𝐹𝐹4 ) where: 𝐹𝐹1 , 𝐹𝐹2 , 𝐹𝐹3 , 𝐹𝐹4 are forces collected from sensors Non-standardized regression coefficients (B): provide regression coefficients that reflect the change of the dependent variable accoeding to an independent variable 2.2 Linear regression analysis Linear regression method is a method of analyzing the relationship between the dependent variable Y (in our method, Y is the position of the CoG) with one or more dependent variables X (the body’s measurements), based on a set of input Standardized regression coefficients (β): reflect the coefficients of independent variables on the dependent coefficients, which have been 58 Journal of Science & Technology 139 (2019) 057-061 standardized to remove constants In all regression coefficients, which independent variables has the largest β, meaning that variable mostly affects to the change of the dependent variable Therefore, when proposing a solution, much attention should be paid to factors that have a large β coefficient After the data has been collected, the processing method is identified and the recommendations are made, we have conducted and obtained the following results Proposition 1: the dependency of CoG on the height (h) The variance inflation factor (VIF) coefficient: this value is used to check the phenomenon of multicollinearity Multicollinearity is the phenomenon that independent variables have a strong correlation with each other The regression model, which happens to be multicollinear, will cause many indicators to be misleading, resulting in quantitative analysis that no longer has much meaning If VIF